Let Gamma(n)(A) denote the abstract simplicial complex whose elements are dissections of a convex (n + 2)-gon. Lee proved that Gamma(n)(A) is the boundary complex of a convex polytope, now known as the associahedron. Simion constructed a type-B associahedron whose faces correspond to centrally symmetric dissections of a (2n + 2)-gon. In this paper, we define a partial order on the set of centrally symmetric triangulations whose Hasse diagram is the I-skeleton of the simple B-associahedron and explore properties of this poset, including encodings, self-duality, and chain length. We also establish lattice failure and goodness. (C) 2004 Elsevier B.V. All rights reserved.
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